Page 60 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 60
INVITED SPEAKERS
interesting results about the topology of symplectic fillings of contact 3-manifolds. In this talk,
I will present my contribution to the subject at hand based on joint work with several coauthors
during the past 20 years.
Nonstandard finite elements for wave problems
Ilaria Perugia, ilaria.perugia@univie.ac.at
University of Vienna, Austria
Finite elements are a powerful, flexible, and robust class of methods for the numerical ap-
proximation of solutions to partial differential equations. In their standard version, they are
based on piecewise polynomial functions on a partition of the domain of interest. Continuity
requirements are possibly dictated by the regularity of the exact solutions. By breaking these
constraints, new methods that are specifically tailored to the problem at hand have been devel-
oped in order to better reproduce physical properties of the exact solutions, to enhance stability,
and to improve accuracy vs. computational cost. Nonstandard finite element approximations of
wave propagation problems based on the space-time paradigm will be the focus of this talk.
Scaling Optimal Transport for High dimensional Learning
Gabriel Peyré, gabriel.peyre@ens.fr
CNRS and ENS, PSL University, France
Optimal transport (OT) has recently gained lot of interest in machine learning. It is a natural
tool to compare in a geometrically faithful way probability distributions. It finds applications in
both supervised learning (using geometric loss functions) and unsupervised learning (to perform
generative model fitting). OT is however plagued by the curse of dimensionality, since it might
require a number of samples which grows exponentially with the dimension. In this talk, I will
explain how to leverage entropic regularization methods to define computationally efficient loss
functions, approximating OT with a better sample complexity. More information and references
can be found on the website of our book “Computational Optimal Transport”.
Finite groups of birational transformations
Yuri Prokhorov, prokhoro@mi-ras.ru
Steklov Mathematical Institute, Russian Federation
I survey the classification theory of finite groups of birational transformations of higher-dimen-
sional algebraic varieties. This theory has been significantly developed during the last 10 years
due to the success of the minimal model program. I concentrate on certain properties of these
groups in arbitrary dimension. Also, I am going to discuss the three-dimensional case in more
details.
58
interesting results about the topology of symplectic fillings of contact 3-manifolds. In this talk,
I will present my contribution to the subject at hand based on joint work with several coauthors
during the past 20 years.
Nonstandard finite elements for wave problems
Ilaria Perugia, ilaria.perugia@univie.ac.at
University of Vienna, Austria
Finite elements are a powerful, flexible, and robust class of methods for the numerical ap-
proximation of solutions to partial differential equations. In their standard version, they are
based on piecewise polynomial functions on a partition of the domain of interest. Continuity
requirements are possibly dictated by the regularity of the exact solutions. By breaking these
constraints, new methods that are specifically tailored to the problem at hand have been devel-
oped in order to better reproduce physical properties of the exact solutions, to enhance stability,
and to improve accuracy vs. computational cost. Nonstandard finite element approximations of
wave propagation problems based on the space-time paradigm will be the focus of this talk.
Scaling Optimal Transport for High dimensional Learning
Gabriel Peyré, gabriel.peyre@ens.fr
CNRS and ENS, PSL University, France
Optimal transport (OT) has recently gained lot of interest in machine learning. It is a natural
tool to compare in a geometrically faithful way probability distributions. It finds applications in
both supervised learning (using geometric loss functions) and unsupervised learning (to perform
generative model fitting). OT is however plagued by the curse of dimensionality, since it might
require a number of samples which grows exponentially with the dimension. In this talk, I will
explain how to leverage entropic regularization methods to define computationally efficient loss
functions, approximating OT with a better sample complexity. More information and references
can be found on the website of our book “Computational Optimal Transport”.
Finite groups of birational transformations
Yuri Prokhorov, prokhoro@mi-ras.ru
Steklov Mathematical Institute, Russian Federation
I survey the classification theory of finite groups of birational transformations of higher-dimen-
sional algebraic varieties. This theory has been significantly developed during the last 10 years
due to the success of the minimal model program. I concentrate on certain properties of these
groups in arbitrary dimension. Also, I am going to discuss the three-dimensional case in more
details.
58
